Function estimation is a branch of mathematics having many real world applications. For example, function estimation may be applied to a finite number of noisy measurements (or "observations") for the purpose of approximating a function that describes the phenomenon being measured. Existing techniques of function estimation generally use the expansion: ##EQU1## where f(x) is the approximating function, .phi..sub.i (x) are a plurality of a priori chosen functions, .alpha..sub.i are scalars, and "N" is the number of terms in the expansion. Accordingly, to estimate a function using equation (1), one must estimate the scalars .alpha..sub.i. The equation may be readily applied to one or two dimensional data, however its application to data of three or more dimensions is limited by the "curse of dimensionality".
The curse of dimensionality is well known among mathematicians. It refers to the exponential increase in complexity of the estimating function that occurs as the dimensionality of the data being estimated increases. For example, if a one dimensional curve may be estimated with reasonable accuracy by using 20 terms (N=20), then the estimation of a two dimensional surface with reasonable accuracy requires 20.sup.2 terms (N=20.sup.2). A three dimensional surface requires 20.sup.3 terms, and so on. Thus, as the dimension of the function to be estimated increases, the number of terms required rapidly reaches the point where even the most powerful computers can not handle the estimation in a timely manner.